diff --git a/mesonbuild/modules/cuda.py b/mesonbuild/modules/cuda.py
index b52288ab5..690053868 100644
--- a/mesonbuild/modules/cuda.py
+++ b/mesonbuild/modules/cuda.py
@@ -13,14 +13,13 @@ from ..interpreter.type_checking import NoneType
 from . import NewExtensionModule, ModuleInfo
 
 from ..interpreterbase import (
-    ContainerTypeInfo, InvalidArguments, KwargInfo, flatten, noKwargs, typed_kwargs,
+    ContainerTypeInfo, InvalidArguments, KwargInfo, flatten, noKwargs, typed_kwargs, typed_pos_args,
 )
 
 if T.TYPE_CHECKING:
     from typing_extensions import TypedDict
 
     from . import ModuleState
-    from ..compilers import Compiler
 
     class ArchFlagsKwargs(TypedDict):
         detected: T.Optional[T.List[str]]
@@ -95,17 +94,19 @@ class CudaModule(NewExtensionModule):
 
         return driver_version
 
+    @typed_pos_args('cuda.nvcc_arch_flags', (str, CudaCompiler), varargs=str)
     @typed_kwargs('cuda.nvcc_arch_flags', DETECTED_KW)
     def nvcc_arch_flags(self, state: 'ModuleState',
-                        args: T.Tuple[T.Union[Compiler, CudaCompiler, str]],
+                        args: T.Tuple[T.Union[CudaCompiler, str], T.List[str]],
                         kwargs: ArchFlagsKwargs) -> T.List[str]:
         nvcc_arch_args = self._validate_nvcc_arch_args(args, kwargs)
         ret = self._nvcc_arch_flags(*nvcc_arch_args)[0]
         return ret
 
+    @typed_pos_args('cuda.nvcc_arch_readable', (str, CudaCompiler), varargs=str)
     @typed_kwargs('cuda.nvcc_arch_readable', DETECTED_KW)
     def nvcc_arch_readable(self, state: 'ModuleState',
-                           args: T.Tuple[T.Union[Compiler, CudaCompiler, str]],
+                           args: T.Tuple[T.Union[CudaCompiler, str], T.List[str]],
                            kwargs: ArchFlagsKwargs) -> T.List[str]:
         nvcc_arch_args = self._validate_nvcc_arch_args(args, kwargs)
         ret = self._nvcc_arch_flags(*nvcc_arch_args)[1]
@@ -123,21 +124,15 @@ class CudaModule(NewExtensionModule):
             return [c.detected_cc]
         return []
 
-    def _validate_nvcc_arch_args(self, args, kwargs: ArchFlagsKwargs):
-        argerror = InvalidArguments('The first argument must be an NVCC compiler object, or its version string!')
+    def _validate_nvcc_arch_args(self, args: T.Tuple[T.Union[str, CudaCompiler], T.List[str]], kwargs: ArchFlagsKwargs):
 
-        if len(args) < 1:
-            raise argerror
+        compiler = args[0]
+        if isinstance(compiler, CudaCompiler):
+            cuda_version = compiler.version
         else:
-            compiler = args[0]
-            if isinstance(compiler, CudaCompiler):
-                cuda_version = compiler.version
-            elif isinstance(compiler, str):
-                cuda_version = compiler
-            else:
-                raise argerror
+            cuda_version = compiler
 
-        arch_list = [] if len(args) <= 1 else flatten(args[1:])
+        arch_list = args[1]
         arch_list = [self._break_arch_string(a) for a in arch_list]
         arch_list = flatten(arch_list)
         if len(arch_list) > 1 and not set(arch_list).isdisjoint({'All', 'Common', 'Auto'}):